If $a={10}^3\times 0.0099$ and $b={10}^{-2}\times 110$, then  $\sqrt{\frac{a}{b}}$is

$a={10}^3\times 0.0099$ and  $b={10}^{-2}\times 110$

$a=1000\times \frac{99}{10000}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}b=\frac{1}{100}\times 110$

$a=\frac{99}{10}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}b=\frac{11}{10}$

$\sqrt{\frac{a}{b}}=\sqrt{\frac{\raisebox{1ex}{$99$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}}=\sqrt{\frac{99}{11}}=\sqrt{9}=3$